eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2018-06-20 6 3 93 97 10.12691/tjant-6-3-5 TJANT2018635 article Ali Boussayoud 1 Mourad Chelgham chelghamm@yahoo.fr 2 Souhila Boughaba 3 LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria LMAM Laboratory and Departement of Mathematics, Freres Mentouri Constantine1 University, Algeria Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeri In this paper, we introduce a new operator in order to derive some properties of homogeneous symmetric functions. By making use of the proposed operator, we give some new generating functions for Mersenne numbers, Mersenne numbers and product of sequences and Chebychev polynomials of second kind. http://pubs.sciepub.com/tjant/6/3/5/tjant-6-3-5.pdf Mersenne numbers Generating functions Symmetric functions